Sleep only one monitor in multi-monitor setup

I hope this is in the right place. I have a Windows 7 PC running a dual monitor setup (HDMI and DVI). I want one monitor to stay on permanently and the other to go to sleep after 10 mins. Background for why is below, if interested. I've searched high and low and am usually quite tech savvy, but this has me completely stumped! Any help appreciated.

Background. My dual monitor setup is actually, one monitor and one AV amp (connected to my TV). The issue is that because I output both sound and video through HDMI to my AV amp, when the monitors go to sleep, the sound stops coming out of my speakers (it's part of the HDMI spec, the video is used as the sync signal for HDMI audio, which means when the video signal stops, the audio does too!!!). This is really annoying. I want my main monitor to go to sleep to save power and stop burn-in, but I want my sound to keep playing. I've already had to tape over the "detection" pin on the HDMI cable to stop it redetecting my amp every time I turn it on because there is no software solution. Unbelievable!! So much for PC's moving into the living room!

The only solution that I know that should work is to just not use the HDMI audio. Run an aux audio line from the computer with the HDMI line, switch the audio on the computer to the local subsystem and use a separate audio in connection on the AV unit (assuming you are using discrete speakers of course).